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Answer :
To find the length of the radius of circle F, we start by looking at the equation of the circle, which is [tex]\((x+6)^2 + (y+8)^2 = 9\)[/tex].
The standard equation for a circle is:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
where [tex]\((h, k)\)[/tex] is the center of the circle, and [tex]\(r\)[/tex] is the radius.
By comparing the given equation [tex]\((x+6)^2 + (y+8)^2 = 9\)[/tex] with the standard equation, we identify:
- The center of the circle [tex]\((h, k)\)[/tex] is [tex]\((-6, -8)\)[/tex], but this isn't needed to find the radius.
- The right side of the equation represents [tex]\(r^2\)[/tex], which is [tex]\(9\)[/tex].
To find the radius [tex]\(r\)[/tex], you take the square root of [tex]\(9\)[/tex], because [tex]\(r^2 = 9\)[/tex].
So, the radius [tex]\(r\)[/tex] is:
[tex]\[
r = \sqrt{9} = 3
\][/tex]
Therefore, the length of the radius of circle F is [tex]\(3\)[/tex].
The correct answer is A. 3
The standard equation for a circle is:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
where [tex]\((h, k)\)[/tex] is the center of the circle, and [tex]\(r\)[/tex] is the radius.
By comparing the given equation [tex]\((x+6)^2 + (y+8)^2 = 9\)[/tex] with the standard equation, we identify:
- The center of the circle [tex]\((h, k)\)[/tex] is [tex]\((-6, -8)\)[/tex], but this isn't needed to find the radius.
- The right side of the equation represents [tex]\(r^2\)[/tex], which is [tex]\(9\)[/tex].
To find the radius [tex]\(r\)[/tex], you take the square root of [tex]\(9\)[/tex], because [tex]\(r^2 = 9\)[/tex].
So, the radius [tex]\(r\)[/tex] is:
[tex]\[
r = \sqrt{9} = 3
\][/tex]
Therefore, the length of the radius of circle F is [tex]\(3\)[/tex].
The correct answer is A. 3
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